 Hi, I'm Zor. Welcome to Nezor Education. Today I would like to spend some time and talk about the very foundation of special theory of relativity, mainly two postulates axioms, whatever, which were formulated by Einstein as some kind of a preamble to his fundamental work he published in 1905. Now, this lecture is part of the course called Relativity for All, presented in Unizor.com. On the same website you will find two prerequisite courses, Maths for Teens and Physics for Teens. Maths and Physics on the classical level are absolutely mandatory to study theory of relativity. So, either you study somewhere else or you can study it on this website, but anyway, these are fundamental knowledge which is definitely needed. Now, the website is totally free. There are no advertisement. Every lecture has detailed notes, which basically resemble the textbook, so you have an advantage of hearing basically, of watching the lecture itself, and at the same time or later on or before that you can read the text, which is kind of more accurate, maybe, than what I'm talking or I'm explaining, maybe slightly differently, though I don't think so. There are problems, there are exams on the website, so I do recommend you to watch this lecture and every other lecture of the course from the website. Okay. Now, first, let's talk about something which is absolute versus relative. We're talking about relative, theory of relativity, right? So, we have to really understand what relative actually means. Well, speaking about absolute first, there are certain things which seem to be absolute sometime ago. Let's say, some time ago, people were thinking that the Earth is flat. So, the concept of a vertical was basically absolute. It was exactly the same for everybody. Everybody knew what vertical is when the flat Earth was, model was actually in favor. Now, when people realized that the Earth is round, obviously vertical for people who are in northern hemisphere is not exactly the same as in southern hemisphere. Or actually, two people wherever they are, as long as the place of their standing is significantly different, they will have different directions of vertical. So, this is just a, you know, half joking example, obviously. But things are much more serious about relativity of position, for example. Again, up until certain time, people were thinking that the Earth is the center of the universe. And that makes this point absolute. So, like, everything is circling around the Earth. And it was Copernicus who actually suggested that the Earth goes around the Sun. Well, he did not venture to galaxies and metagalaxy, etc. But nevertheless, it was already a significant shift from the absolute position which our planet actually possessed before him to something relative to something else. So, that was one of the first kind of manifestation of the concept of relativity. In this case, it's a relative position. If there are two people, for example, standing on Earth, there is no way to say that one is more advantageous than another from the scientific standpoint. I don't mean anything else. So, position is relative. There is no absolute zero, let's say, absolute beginning of the universe. Now, later on, we have come up to another very important concept of relativity, relativity of the movement. And primarily, I think, Galileo contributing to this. If object A moves relative to object B, at the same time, object B is moving relative to object A in the opposite direction. So, movement is also relative. So, everything related to space, actually, people realize it's relative to something else, to other position, to other movement, to other whatever. And that was kind of a natural way of thinking about our world. So, space was considered as really something which can be related as relative to all the pieces, all the pieces are relative to each other when combined into our universe. So, that was basically the beginning of the relativity. Now, the second thing which is related to the first is, and that's primarily because of works of Galileo, if there is certain law, physical law, which manifests itself in some way, the same kind of law and the same kind of expression of that law, mathematical expression of that law, for example, can be observed in another system which is moving relative to the first system uniformly along the straight line, as long as there are no external forces acting on these two systems. So, the perfect example is, if you are on the train and the train is just staying on the station, and there is another train next on the next track, and it's very, very slowly moving. At some point, I think you have experienced that yourself, that it's kind of difficult to say we are standing and that train is moving or that train is standing and we are moving, as long as we don't look into other windows, as long as we just look at the two trains, you look at this train and this train is moving, you might think that your train is moving. So, this leads us to the concept of inertial frames, which we were talking about, and Galileo and transformation from one inertial frame to another. So, the relativity of space leads us to this first principle of the future theory of relativity, the principle of relativity, which basically states that all the laws of physics are exactly the same in two different inertial frames moving uniformly along the straight line, one against another. Now, it's not really necessary to say that it's, let's say, a system beta is moving relative to alpha because at the same time alpha is moving relative to beta, right? So, basically it's all relative. This is the first principle of relativity and expression of these physical laws, quantitative expression, like mathematical equations, in two different inertial frames moving with uniform speed relative to each other, these mathematical expressions must be the same as well. That's our experience, it's based on observation, it's based on the theory, the three new-tones laws of mechanics, for example, conforms this, etc. So, this is relativity of space and that was basically fine with physicists, with everybody else, everybody understood what this principle of relativity is and it actually became the first postulates of the theory of relativity, which Einstein developed. It was done, basically, at that particular time everybody understood it. Now, what is necessary for the system, for the inertial system, let's say? What we need is Cartesian coordinates and the clock. Basically, these two are sufficient to transfer our physical law into mathematical quantities. So, as long as we have coordinates, we have quantitatively evaluating, we can quantitatively evaluate position, movement, again with the clock at our disposal, we have timing, which means we have to define speed, acceleration, whatever. So, everything is basically sufficient. So, whenever we are talking about inertial system or inertial reference frame, we are talking about certain Cartesian coordinates and the clock, which is hooked into this system. And that, my last statement was very important, because up until 19th century, including, people did not consider clock as being relative. Time was absolute. So, the time on the clock in one inertial frame should actually be exactly the same as clock in another. People did not think about anything, which can actually affect the clocks. As long as they are ideal clocks, as long as they are synchronized, you can put one clock into one system, another clock into another system, which is moving, and the whatever is on the clock will always be the same. So, the time is absolute. That was the classical physical approach. Space was relative, time was absolute. That's very important. And principle of relativity, which is mostly related in the past to the space, was accepted by everybody, including theory of relativity. Okay. Let's go next. One of the consequences from principle of relativity related to space is that there is no such thing as absolute rest. So, there is no such system which absolutely moves with the speed zero. Why? Well, because there is always some other system which moves somehow, but relative to that system, this system is not really standing still. It's also moving. It all depends which system we're related to. So, there is no absolute rest. And then we have problems. Now, the problems were related to the fact that there were Maxwell equations for electromagnetic field, which basically dictates the speed of light as dependent on only characteristics of the medium. Permiability and permittivity. Electric and magnetic properties of the medium where the light is propagating. So, vacuum, for example, has its own epsilon and mu, electrical permittivity and magnetic permeability. And these two constants, which are constants, absolute constants, it's just a number basically, they are sufficient to determine the speed of light. So, that was something kind of strange. Why? Well, because we used to think that everything is relative, which means the speed is supposed to be relative to, let's say, the source of the speed. So, if I'm moving on the platform and throw a ball with some speed which I am capable of, now the real speed of the ball will be a sum of my speed plus speed of the platform I'm moving on if the platform is moving. So, that was kind of a natural assumption and it worked quite well, actually, with all the calculations and practical experience. But with light, it seems to be different. So, the Michelson experiment basically proved that no matter which direction, no matter how the source of light is moving, and he was using Earth as the source of light because Earth is moving. So, he directed the rays into different directions and considering that the Earth is moving in space with a substantial speed like 30 kilometers per second, he expected that the timing would be different. However, that was not observed. Speed of light was exactly the same. No matter where you go, no matter which direction you go, with the direction of the Earth, against the direction of the Earth, the timing for the same distance was exactly the same. And by that time, the instruments were precise enough to distinguish even the smallest deviation from this. So, people repeated these experiments many times and every experiment showed exactly the same thing. Speed of light is constant. No matter how source of light is moving, one direction, another direction, standing still relative to something, it doesn't really matter. Speed of light is always the same. Well, not exactly the same because I said it depends on the medium. So, let's say you have a glass. So, the light goes through the glass and the speed of light in the glass is different because the properties of the glass are different. But whenever it exits the glass, the speed is basically the same as it was before, which is kind of different because if you, for example, if you shoot a bullet through relatively thin wooden plank, for example, after it goes through this, it goes out to air out there, but then the speed will be reduced. So, after it hits something like an obstacle, it goes, it penetrates it, but then it loses the speed. Light on the other hand, after it leaves the glass where the speed was less in the air, it goes back into the air and the speed is restored back. So, that was another kind of thing, strange. So, there are many strange things about light. And what's probably most kind of upsetting, I would say, that the constancy of the speed of light contradicts the first principle, the principle of relativity. And let me explain how. Let's say you are on a platform. So, here is you. Platform is moving with the speed V and you're throwing the ball with speed S. So, let's say this is L and this is L. You're in the middle. L to the left, L to the right. Now, let's talk about classical physics. What's your speed relative to the earth? What's the ball speed relative to the earth? Well, obviously, it's V plus S. During certain time, let's call it T front, with this speed, it will hit the wall of this platform, right? Now, what's the distance? The distance is initial L plus additional distance, which during exactly the same time, my platform moves. So, that should be equal to L plus V times T F. When this T F is equal to V times T F, V times T F cancels out. So, I have L and S T F here. So, it will be L divided by S. Well, this is fine because if you are in a standing still platform relative to earth, that would be exactly the same answer. Distance divided by speed. Nothing wrong about this. Now, let's go and hit the ball backwards. The speed of the ball will be V minus S. The time will be T back. The time it reaches the back end. Now, let's say this is coordinate L, this is coordinate zero, this is minus L, this is plus L of this point. So, coordinates of this point would be minus L plus V T F, from which T B is equal to, again, V T back cancels out. This minus, this minus doesn't matter. So, it's L over S. Same thing. So, the time it reaches the front wall or the back wall, whether we are moving or standing still, doesn't really matter. It does not depend on speed V. Great. That's how it's supposed to be. That's the principle of relativity. The result of experiment does not depend on whether a platform is moving or not. Terrific. Let's go to light. For example, it's not the ball which I'm throwing with a certain speed S. Let's consider this is the beam of light and let's again calculate the same thing. What's the problem here? The problem is that the speed of light is always the same, constant C, which in the vacuum is about 300,000 millimeters per second. So, it's not V plus S, which is the speed of beam of light. It's always C. So, I have C times T front equals L plus V T front, from which T front is equal to L divided by C minus V. This goes to this and T is factoring out. Now, in this case, I have, again, I do not have B minus S at the speed of beam of light. I still have C times T B is equal to minus L plus V T B from which it's minus S, actually, because we are going this way. It's minus S minus C, which means T B is equal to L to this, C to this, L divided by C plus V. Look at these. These are two different times. If V is not equal to zero, it's two different times, which means by comparing these two, I can always find out that we are moving or not moving. If these things are different, it means we are moving because if we are standing still, if B is equal to zero, they are equal to each other. So, in a standing still platform, this experiment would show the same time the beam is reaching the back and front. But if the platform is moving, it's not. So, there is something which we can always say that there is an absolute rest. So, whenever these two timings on this platform are the same, that means we are at rest. Absolute rest, which is contradiction to theory of relativity. We don't have something like absolute rest. So, this is something which was kind of all these thoughts were gathered by Einstein as, well, something which needs to be resolved. Physicists kind of knew all this, obviously, but they did not have any valid explanation until he in 1905 came up with explanation related to not only concept of relativity of space, but also relativity of time. And in his article, very important article, which he published at that time, he basically explained his thoughts. And it was very logical from the first principle, the principle of relativity, and the second principle, which is constancy of the speed of light. Just from these two, as axioms, he derived purely mathematically, using some sort of experiments, but purely mathematically, he derived the formulas for something which we now call time dilation, and basically transformation of coordinates from one inertial system into another. Now, we will talk about this in subsequent lectures, but what's interesting is that the equations which he came up with, equations which are transforming coordinates, and time, and time, very important from one system to another, one inertial system to another. So these equations of transformation are exactly the same as another very famous physicist Lawrence, before him, derived as transformation which retains the Maxwell equation invariant from one inertial system to another. He, Lawrence, basically suggested these purely mathematical formulas, how to transfer coordinates, space coordinates, and time from one system into another, which leave Maxwell equations basically intact. So they look exactly the same in two different systems, and that was a great achievement actually, and a great confirmation that the theory is correct. You see, if you come up with the same result completely differently, then it actually proves more convincingly, I would say, that the results are correct. Okay, so that was the most important part of physics, I would say, of the 20th century. But one of the most important, there is another theory, obviously, there is a continuation of this special theory of relativity, which is called general theory of relativity, which involves gravitation and bending of the space. So it's not really Cartesian, so to speak, and then quantum physics came up. So I mean, there are definitely huge discoveries in the 20th century physics, but that was probably the first major one out of, let's say, three or four. Okay. All right, now I suggested to read the notes for this lecture, so go to unisor.com, go to relativity for all course, and in a topic is called Einstein View, that's the menu item, and this would be the first, basically, kind of introductory, what kind of foundation, what kind of postulates were put into the theory of relativity, two postulates again. One is principle of relativity, that all the laws are supposed to be the same in inertial frames, and the second one is constants of the speed of light. So thank you very much, and good luck.